Alteration of the geometry of a model has been known in the art. Common applications of geometry transformation include moving, scaling and rotating models, which merely apply a linear transformation to the model's geometry. Nothing in these simple transformations indicated the use of arbitrary function composition to perform more complicated, arbitrary transformations.
Geometric transformation using a single specific function is also known in the art. For example, U.S. Pat. No. 4,821,214 to Sederberg [Sederberg] demonstrates the transformation of a model defined by a grid of control points by a single specific function. [Sederberg] does not indicate the ability to perform a transformation using any arbitrary function, and [Sederberg] does not disclose defining the model using procedural surfaces, curves and positions to allow arbitrary function composition. In order to define a shape, [Sederberg] requires the user to define a set of control points that approximate the shape. In order to achieve accuracy required for many operations such as Computer Aided Manufacturing (CAM), a large number of control points must be defined which makes working with the model difficult. [Sederberg] does not disclose representing the geometry of a shape as a set of functions which allow for more accurate and easier manipulation.
Similarly, the Pro-Engineer CAD modeling product by Parametric Technologies Corporation [PTC] contains a bend function which allows a user to perform a specific, pre-defined bend transformation function. Nothing in [PTC] discloses using a general function composition mechanism to allow transformation with an arbitrary, user-defined function.
Because of the limitations of the prior art, there exists a continuing need to allow geometric transformation in CAD applications using a generalized mechanism for applying arbitrary functions.